SamizdatMath

On September 18th, 2015, New York City standup comedian Matt Little recorded a video of a rat dragging a slice of pizza down the stairs at the First Avenue L train station in Manhattan. On September 21st, Little uploaded the video to his Instagram and YouTube accounts with a bemusing description comparing the rodent to Master Splinter from the Teenage Mutant Ninja Turtles (shown below). Within the first 24 hours, the video garnered over two million views. This is an investigation into the perime

To quote Charles Dickens (from The Pickwick Papers) “What fresh misery is this?” This is what happens when you have time on your hands and you’re thinking to yourself, “well, how can I bring bles’sed torment unto my students this week?” Many (many) years ago I had a student in my sixth grade class (you probably had them) who would respond to any “do now” problem with a quick look and the brag “oh, this is so easy!” And then after fumbling his way through 3 or 4 methods, all featuring a lapse of

Back in the 1980s (before most of you were born), the A & W hamburger restaurant chain tried to go head to head with McDonalds' new "quarter pounder" by creating and marketing a "⅓ pound hamburger." It was a spectacular flop. A research company hired to find the source of the problem found out that half of the people surveyed thought that there was less meat in a ⅓ lb. burger than a ¼ lb. burger because, well, "3 is less than 4." The burger was renamed the "Big Papi" and continued to be sold b

This is an investigation that first appeared in Harold Jacobs "Mathematics: A Human Endeavor." It uses a simplified billiard table with four corner pockets to model ratio and proportions, as well as give students the opportunity to conduct original research on different questions that arise from the investigation. Although I only showed the first student page and answer sheet, there are actually many different sections to this investigation: the first is an exploration section where students con

What goes better with equivalent fractions than CHANUKAH! Hanukah Harry is carrying a fraction in his bag; surrounding him are equivalent fractions that are missing a numerator or denominator. Alas, one of them is NOT KOSHER and cannot be completed! For example, if there is a fraction 1/3 and ?/5 is one of the choices, it can't be completed, because 3rds can't be turned into 5ths. SO MUCH FUN your kids will love it finding treif fractions! Customer Tips: How to get TPT credit to use on future p

No, it's not a "scoot" game or a tradition "bingo" game; this is an estimation strategy game where students use 4 numbers to create a fraction and then turn it into a decimal (either by hand or using a mental strategy, NOT LONG DIVISION!), round it off (if needed) and then find a square that satisfies that decimal. However, there are many ways to choose a square: some clues are "between" clues ("between .2 and .3") or "exact" clues ("exactly .25") or "less than" clues ("less than .2") which mea

Did you know that the ninths fractions can easily be converted by taking the numerator and turning it into a repeating decimal? For example, 4/9 = .444... and 8/9 = .888....? Did you know that the 11ths fractions cycle through the 9 times tables through the numerator? 5/11 = .4545.... and 7/11 = .6363.... These are great patterns to know because it can save your students hours of tedious calculations when converting fractions to decimals. Since patterns are the "language of mathematics" then s

This is an activity that I used as a kind of “warm-up” to a unit on fractions with my 5th graders; I wanted to relate fractions to ratios, as well as see what the classes had remembered from the previous year. I gave out this activity, put the students in dyads (that’s groups of 2, for those of you who have forgotten their Greek, it means students work in pairs of 2.) They complete the activity sheet and then write up a summary of their findings, which they post on a wall. You can use this acti

This is a 4 page assessment for fifth graders, although sixth and seventh graders will find it challenging, as will advanced 4th graders. As stated, it is balanced between concepts, skills and problem solving (as opposed to "regular" tests which focus on skills like creating equivalent fractions, "reducing" fractions and adding/subtracting fractions.) Here are the features of this exam: 1) It uses a variety of models, including an area model using pattern blocks, and the linear model on a numb

This is a fun approach to understanding the importance of ratios and proportions when working with visual arts: I took the famous Gilbert Stuart photo and cropped it so that it would be 2" x 3" and then made enlargements based on adding 1" to both the width and the height. The result is a distorted George that looks like he has had a tooth removed; Seriously, the idea here is that your students look at a series of photos, measure them in inches, and then organize that information into a chart w

Three different "EZ-CUT" and paste activities with fractions, decimals and percents. Activity 1: Students cut out proper fractions and match them to equivalent terminating and non-terminating decimals. Some decimals are rounded to the nearest thousandth, others use a vinculum or ellipse to show that it repeats. Activity 2: Students cut out proper and improper fractions and match to equivalent decimals, both terminating and non-terminating. Students round off to the nearest thousandth when nec

I love those "cut n' paste" activities, but I wonder how much time is wasted by students who have to cut out all those little pieces along the lines and then maneuver them into place. What good are these activities if the students spend 20 minutes cutting and only 10 minutes "thinking" about math? In my version of a "fractions to percents" cut n' paste, I've designed the pieces to be cut out with a minimum of cutting, so that your students can focus on actually "doing the math." By placing the

This is the BEST "cut n' connect" equivalent fractions activity ever. Here's why: 1) Multiple representations of fractions: all the others use the awful "pie" model. This one uses line, area and groups to model fractions from halves up to twelfths. 2) Students do most of the work: Many other versions come "pre-digested," that is, the pieces and fractions are all filled in. In this one, the students have to fill in the missing numerator, denominator or shade in the fraction before cutting out

I love those "cut n' paste" activities, but I wonder how much time is wasted by students who have to cut out all those little pieces along the lines and then maneuver them into place. What good are these activities if the students spend 20 minutes cutting and only 10 minutes "thinking" about math? In my version of a "fractions to decimals" cut n' paste, I've designed the pieces to be cut out with a minimum of cutting, so that your students can focus on actually "doing the math." By placing the

Your kids need a reason to convert fractions to decimals? Or decimals to fractions? Here's a fun activity to get your kids psyched to do this: on one side of the page there are mixed numbers (whole numbers and fractions) that have to be converted to decimals so that the amount can be entered on the gas pump. There are "easy" examples with common terminating fractions, as well as "harder" examples where the decimal has to be calculated to the nearest 10,000th in order to be rounded off to the nea

This is a fun little activity that you can do in a class period, or just give for homework, and it will get your kids to think carefully about fractions, most likely beyond the junk that is in whatever textbook you are using. It would also be excellent as an assessment of your students’ basic understanding of how fractions work. The idea is this: do your students have a basic understanding of how fractions work? Do they REALLY? This is how you do it in 5 questions. In questions 1 and 2, we look

I was sitting in a fifth grade math class yesterday afternoon watching a teacher do what I thought was pretty good lesson on fractions. As the kids struggled to figure out how to compare fractions, I was asked by a student whether fractions that had small denominators were larger. I answered, “well, that really depends....” and without missing a beat, that same student said, “so, if the numerator is big, then the fractions must be big too....” I replied, “well, that depends as well....” to whic

This is a collection of 8, count 'em, 8 different "Yogi-isms" that have to do with some mis-statement of a mathematical concept, featuring a writing prompt in the form of a letter to Yogi Berra explaining his mathematical mistake. The statements include: "90% of baseball is mental; the other half is physical." “You have to give 100 percent in the first half of the game. If that isn’t enough, in the second half, you have to give what is left.” When Yogi ordered a pizza, the waitress asked h

This activity uses a classic Abbot & Costello comedy routine to explain the concept of comparing numbers using ratios. This short video, which is available on YouTube, is about 5 minutes long and features a routine by Abbot and Costello where they compare the age of two people using the difference in their age (40 and 10) to create a ratio ("I am 4 times older than the 10 year old) and then re-calculates the ratio after 5 has been added to create 45:15, which is 3:1 when simplified. There is an

What goes better with equivalent fractions than ZOMBIES! And what goes better with zombies than Valentine's Day? Each of these ghouls represents a fraction; surrounding them are equivalent fractions with heart-shaped zombie brains that are missing a numerator or denominator. Alas, one of them is a ZOMBIE and cannot be completed! For example, if there is a fraction 1/3 and ?/5 is one of the choices, it can't be completed, because 3rds can't be turned into 5ths. SO MUCH FUN your kids will love i